Polynomial Estimation of Linear Regression Parameters for the Asymmetric PDF of Errors

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dc.contributor.authorZabolotnii, Serhii
dc.contributor.authorЗаболотній, Сергій Васильович
dc.contributor.authorWarsza, Zygmunt Lech
dc.contributor.authorTkachenko, Oleksandr
dc.contributor.authorТкаченко, Олександр Миколайович
dc.date.accessioned2025-12-01T10:50:00Z
dc.date.available2025-12-01T10:50:00Z
dc.date.issued2018
dc.description.abstractThis paper presents a non-standard way of finding estimates of linear regression parameters for the case of asymmetrically distributed errors. This approach is based on the polynomial maximization method (PMM) and uses the moment and cumulant description of random variables. Analytic expressions are obtained that allow one to find estimates and analyze their accuracy for the degree of the polynomial S = 1 and S = 2. It is shown that the variance of polynomial estimates (for S = 2) in the general case is less than the variance of estimates of the ordinary least squares method, which is a particular case of the polynomial maximization method (for S = 1). The increase in accuracy depends on the values of cumulant coefficients of higher orders of random errors of regression. Statistical modeling (Monte Carlo & bootstrapping method) is performed, the results of which confirm the effectiveness of the proposed approach.
dc.identifier.citationZabolotnii S. V., Warsza Z. L., Tkachenko O. M. Polynomial Estimation of Linear Regression Parameters for the Asymmetric PDF of Errors. Advances in Intelligent Systems and Computing. [Електронне видання]. 2018. № 743. рр. 758-772. DOI: https://doi.org/10.1007/978-3-319-77179-3_75 [Scopus]
dc.identifier.urihttps://link.springer.com/chapter/10.1007/978-3-319-77179-3_75
dc.identifier.urihttps://dr.csbc.edu.ua/handle/123456789/692
dc.publisherSpringer Nature
dc.subjectSOCIAL SCIENCES::Statistics, computer and systems science
dc.subjectMATHEMATICS
dc.titlePolynomial Estimation of Linear Regression Parameters for the Asymmetric PDF of Errors
dc.typeConference paper
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